How to find derivative of this integral?

Question

I need to find the partial derivative

$\frac{\partial}{\partial t} \int_{0}^{\infty}e^{-a\tau}I(x,t-\tau)\ d\tau$.

The answer is given by

$I(x,t)-a\int_{0}^{\infty}e^{-a\tau}I(x,t-\tau)\ d\tau$.

What rule should I use to get the above answer?